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High-order algorithms for Riesz derivative and their applications (II).
- Source :
-
Journal of Computational Physics . Jul2015, Vol. 293, p218-237. 20p. - Publication Year :
- 2015
-
Abstract
- In this paper, we firstly develop two high-order approximate formulas for the Riesz fractional derivative. Secondly, we propose a temporal second order numerical method for a fractional reaction-dispersion equation, where we discretize the Riesz fractional derivative by using two numerical schemes. We prove that the numerical methods for a spatial Riesz fractional reaction dispersion equation are both unconditionally stable and convergent, and the orders of convergence are O ( τ 2 + h 6 ) and O ( τ 2 + h 8 ) , in which τ and h are spatial and temporal step sizes, respectively. Finally, we test our numerical schemes and observe that the numerical results are in good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 293
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 102494904
- Full Text :
- https://doi.org/10.1016/j.jcp.2014.06.007